1. Field of the Invention
The present invention relates to watermarking methods for digital images and videos. More particularly, this invention relates to watermarking methods in the wavelet transform domain.
2. Description of the Prior Art
With the rapid development of information technology, electronic publishing, such as the distribution of digitized images/videos, is becoming more popular. One of the more important issues for the electronic publisher is the ability to obtain and enforce copyright protection. Watermarking is one of the common copyright protection methods that has recently received considerable attention. Watermarking for digital images basically consists of signing an image with a signature or copyright message such that the message is secretly embedded in the image and there is no visible difference between the original and the signed images.
There are two common methods of watermarking: frequency domain and spatial domain watermarks. The present invention focuses on the frequency domain watermarks. Conventional frequency domain watermarking methods are based on the discrete cosine transform (hereinafter xe2x80x9cDCTxe2x80x9d), where pseudo-random sequences, such as M-sequences, are added to the DCT coefficients at the middle frequencies as signatures. This approach, of course, matches the current image/video compression standards well, such as JPEG, MPEG1-2, and the like.
Moreover, it is known that wavelet image/video coding, such as embedded zero-tree wavelet (hereinafter xe2x80x9cEZWxe2x80x9d) coding, has potential to be included in future image/video compression standards, such as JPEG2000 and MPEG4, due to its excellent performance in compression. The basics of EZW can be found in J. Shapiro, xe2x80x9cEmbedded image coding using zerotrees of wavelet coefficientsxe2x80x9d, IEE Trans. On Signal Processing, Vol. 41, pages 3445-3462, December, 1993, which is hereby incorporated in its entirety by reference. The basic idea of EZW is to keep large coefficients with a quantization and throw away small coefficients in the DWT transform domain with a tree-structured addressing. The tree-structured addressing is due to the DWT pyramid decomposition as shown in FIG. 3. Consequently, it is important to study watermarking methods in the wavelet transform domain.
Discrete wavelet transform (hereinafter xe2x80x9cDWTxe2x80x9d) has been extensively studied in the last decade. There are numerous applications of wavelet transforms such as compression, detection, and communications. Basically, in the DWT for a one dimensional signal, a signal is split into two parts, one having high frequencies and one having low frequencies. The part with the high frequencies basically contains the edge components of the signal, while the part with the low frequencies basically contains the smooth areas of the signal. The part with low frequencies is split again into two parts of high and low frequencies. This process is continued an arbitrary number of times, which is usually determined by the application at hand. Furthermore, from these DWT coefficients, the original signal can be reconstructed. This process is called the inverse DWT (hereinafter xe2x80x9cIDWTxe2x80x9d).
The DWT and IDWT can be mathematically stated as follows:
Let H(w)=xcexa3hkexe2x88x92jkw, and G(w)=xcexa3gkexe2x88x92jkw, represent a lowpass filter and a highpass filter, respectively, which will satisfy certain conditions for reconstruction to be stated later. A signal x[n] can be decomposed recursively as shown in equations (1) and (2):                                           c                                          j                -                1                            ,              k                                =                                    ∑              n                        ⁢                          xe2x80x83                        ⁢                                          h                                  n                  -                                      2                    ⁢                    k                                                              ⁢                              c                                  j                  ,                  n                                                                    ;                            (        1        )                                          d                                    j              -              1                        ,            k                          =                              ∑            n                    ⁢                      xe2x80x83                    ⁢                                    g                              n                -                                  2                  ⁢                  k                                                      ⁢                          c                              j                ,                n                                                                        (        2        )            
for j=J+1, J, . . . , J0 where cj+l+k=x[k], k xcex5 Z, J+1 is the high resolution level index and J0 is the low resolution level index. The coefficients cJ0,k, dJ0,k, dJ0+l,k, . . . , dJ,k are called the DWT of signal x[n] where cJ0,k is the lowest resolution part of x[n] and dj,f are the details of x[n] at various bands of frequencies. Furthermore, the signal x[n] can be reconstructed from its DWT coefficients recursively as shown in equation (3):                               c                      j            ,            n                          =                                            ∑              k                        ⁢                          xe2x80x83                        ⁢                                          h                                  n                  -                                      2                    ⁢                    k                                                              ⁢                              c                                                      j                    -                    1                                    ,                  k                                                              +                                    ∑              k                        ⁢                          xe2x80x83                        ⁢                                          g                                  n                  -                                      2                    ⁢                    k                                                              ⁢                                                d                                                            j                      -                      1                                        ,                    k                                                  .                                                                        (        3        )            
The above reconstruction is called the IDWT of x[n]. To ensure the above relationship between IDWT and DWT, the following orthogonal condition on the filters H(w) and G(w) is needed:
|H(w)|2+|G(w)|2=1. 
Examples of H(w) and G(w) are given by:             H      ⁡              (        ω        )              =                            1          2                +                              1            2                    ⁢                                    ⅇ                              -                jω                                      .                          xe2x80x83                        ⁢            and                    ⁢                      xe2x80x83                    ⁢                      G            ⁡                          (              ω              )                                          =                        1          2                -                              1            2                    ⁢                      ⅇ                          -              jω                                            ,
and are known as the Haar wavelet filters.
The above DWT and IDWT for a one dimensional signal x[n] can be also described via two channel tree structured filterbanks as can be seen in FIG. 1.
The DWT and IDWT for two dimensional images x[m, n] can be similarly defined by implementing the one dimensional DWT and IDWT for each dimension m and n separately: DWTn[DWTm[x[m,n]]], as can be seen in FIG. 2.
An image can be decomposed into a pyramid structure, as shown in FIG. 3, and provide various band information, for instance, the low-low, low-high, and-high-high frequency bands. An example of this kind of decomposition with two levels is shown in FIG. 4, where the edges appear in all bands, except in the lowest frequency band, i.e., the corner part at the left and top.
Conventional watermarking methods have several limitations upon which the present invention seeks to improve. For instance, current watermarking methods for digital images and videos, such as the discrete cosine transform (hereinafter xe2x80x9cDCTxe2x80x9d) based approach, are not very robust, do not have multiresolution characteristics, and are not hierarchical in structure, which results in, among other things, high computer loads for distorted images. The present invention solves these problems.
It is, therefore, an object of the present invention to develop a watermarking method for digital images and videos which is based on DWT, and overcomes the limitations of conventional watermarking methods.
It is a further object of the present invention to develop a DWT based watermark which is more robust than conventional methods for common image distortions.
It is yet further another object of the present invention to develop a DWT based watermark which has multi-resolution characteristics.
It is also an object of the present invention to develop a DWT based watermark which is hierarchical and provides reduced computational loads.
These and other objects of the present invention can be better appreciated by referring to the following description and claims taken in conjunction with the accompanying drawings.
The present invention relates to a method of multiresolution watermarking for digital images, which utilizes wavelet transform based watermarking techniques by adding pseudo-random codes (or sequences) to large coefficients located at the high and middle frequency bands of the DWT of the digital image. A peak is then detected to signify a signature of the watermark.
There are three principal advantages with this approach. First, the watermarking method has multiresolution characteristics and is hierarchical. In the case when a received image is not distorted significantly, the cross correlations with the whole size of the image may not be necessary, and therefore, much of the computational load can be saved. Second, the human eyes are generally insensitive to small changes in the edges and textures of an image, but are very sensitive to small changes in the smooth parts of an image. With the DWT, the edges and textures are usually exploited very well in high frequency subands, such as HH, LH, HL, and the like. The large coefficients in these bands usually indicate edges in an image. Therefore, adding watermarks on these large coefficients would be difficult for the human eyes to perceive. Finally, the third advantage is that this approach matches the emerging image/video compression standards. Numerical results show that the watermarking method of the present invention is very robust to wavelet transform based image compressions, such as the EZW image compression scheme, as well as to other common image distortions, such as additive noise, halftoning, and rescaling.